mathcounts problems 43, 50, and 49

Mathematics
Tutor: None Selected Time limit: 1 Day

1. If 2015=101a+19b, for positive integers a and b, what is the value of a+b?

2. If x is postive, what is the result when 8x is doubled and then divided by one half of 8x?

3. What is the area of triangle ABC with vertices A(2,3), B(17,11), and C(17,3)?

Dec 28th, 2014

1.  This can be easily done by trial error.  Try a =16 and b = 21, you get 16 x 101 + 21 x 19 = 2015.

Answer: a= 16 and b= 21

2.  If x is positive, double of 8x is 16x and 1/23 of 8x is 4x.  Divide 16x by 4x , you get 4

Answer:  4

3.  This can be done easily by graphing.  Locate the three given points A, B and C on the x-y plane.

It gives you a right angle triangle with base 8 and height 15. So the area is 1/2 x base x height.

This gives area = 1/2 x 8 x 15 = 60

Answer: 60

Dec 28th, 2014

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